My airport says I'm connected to my DCHP but when I open safari it says I'm not connected to the internet? I have a OS X 10.4.11

Question

Network diagnostics was no help.  I went into the network system preferences and it says that airport is connect to the internet via airport    

Answer 1

Please try each of the steps that follow, in order, until resolved:
STEP 1
Create a New User Account
System Preferences > Accounts
Click "+" to add a new account
Log off, and then, log back on with the new user account.
Try connecting to a Wi-Fi network with your Mac's AirPort.
STEP 2
Delete Preferred Network(s)
System Preferences > Network > Select AirPort > Advanced > AirPort tab
Under Preferred Network, use the minus button to delete the network(s) you regularly use from the list
Delete AirPort Keychain Entries (Note: only applies if you connect to AirPort/Time Capsule routers)
Launch the "Keychain Access" application located in /Applications/Utilities
Click on the "Kind" filter at the top, and look for any "AirPort network password" entries...and delete them.
Restart, or log out then back in.
Add Preferred Network(s)
System Preferences > Network > Select AirPort > Advanced > AirPort tab
Under Preferred Network, click on the plus button to add any preferred network(s).
Restart or log out then back in.
STEP 3
Disable the Mac OS X Firewall
System Preferences > Security > Firewall
Click the "Stop" button.
STEP 4
Move System Configuration Files
(Note: You will have to reestablish your network connections settings.)
Go to Macintosh HD/Library/Preferences
Move the SystemConfiguration folder and com.apple.networkConfig.plist file to the desktop.
Restart your Mac. (Note: OS X will rebuild the files that are now sitting on your desktop. If this doesn't resolve the issue, you can move the folder & .plist file back to their original location.)